The Big Dehn Surgery graph

Genevieve Walsh (Tufts)

Abstract: We study a graph defined as follows. The vertices correspond to closed orientable 3-manifolds. There is an edge between two vertices $v_M$ and $v_N$ if there exists a Dehn surgery along a knot in $M$ yielding $N$. To our knowledge, this graph was first considered by W. Thurston. We present results about the link of $S^3$ in this graph, the global geometry of this graph, and some interesting subgraphs. This is joint work with Neil Hoffman.